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This article is cited in 1 scientific paper (total in 1 paper)
Scattering by a Cylindrical Trap in the Critical Case
R. R. Gadyl'shin Bashkir State Pedagogical University
Abstract:
We study a two-dimensional analog of the Helmholtz resonator with walls of finite thickness in the critical case, for which there exists a frequency which is simultaneously the limit of poles generated both by the bounded component of the resonator and by a narrow communication channel. Under the assumption that the limit frequency is a simple frequency for the bounded component, by using the method of matched asymptotic expansions, we construct asymptotics for the two sequences of poles converging to this frequency. We obtain explicit formulas for the leading terms of the asymptotics of poles and for the solution of the scattering problem.
Received: 06.04.2001
Citation:
R. R. Gadyl'shin, “Scattering by a Cylindrical Trap in the Critical Case”, Mat. Zametki, 73:3 (2003), 355–370; Math. Notes, 73:3 (2003), 328–341
Linking options:
https://www.mathnet.ru/eng/mzm194https://doi.org/10.4213/mzm194 https://www.mathnet.ru/eng/mzm/v73/i3/p355
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Abstract page: | 407 | Full-text PDF : | 186 | References: | 55 | First page: | 1 |
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